New Similarity Reductions and Compacton Solutions for Boussinesq-Like Equations with Fully Nonlinear Dispersion

作     者：YAN Zhen-Ya 

作者机构：Department of Applied Mathematics Dalian University of Technology Dalian 116024 China 

出 版 物：《Communications in Theoretical Physics》 (理论物理通讯（英文版）)

年 卷 期：2001年第36卷第10期

页      面：385-390页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：国家重点基础研究发展计划(973计划) 

主　　题：nonlinear evolution equation, B(m, n) equations, similarity reduction, solitary wave solution,compacton solution 

摘      要：In this paper, similarity rcductions of Boussinesq-like equations with nonlinear dispersion (simply called B(m, n) equations) utt = (un)xx + (um) which is a generalized model of Boussinesq equation uts = (u2)xx + u and modified Bousinesq equation utt = (u3)xx + uxxxx, are considered by using the direct reduction method. As a result,several new types of similarity reductions are found. Based on the reduction equations and some simple transformations,we obtain the solitary wave solutions and compacton solutions (which are solitary waves with the property that after colliding with other compacton solutions, they re-emerge with the same coherent shape) of B(1, n) equations and B(m, m)equations, respectively.